Mathematics Framework: Instructional Strategies and Modeling

June 26, 201412:30-3:30

Outcomes/Agenda• Explore multiple instructional

models that will be required for successful CCSS implementation.

• Discuss a variety of strategies needed to support students in understanding the mathematics being addressed.

• Understand how different instructional strategies support the eight mathematical practices and 21st Century skills.

Opening Task

• As a table group or grade span:– Select an opening task.

• Migdalia’s Savings (grade 2)• After School Job (grades 4/5)• Ms. Olsen’s Sidewalk (grade 7)• Three-Second Rule (high school)

– Complete the task on your own.– Share how you completed the task.

Instructional Strategies

• Kid Snippets “Math Class”• https://

www.youtube.com/watch?v=KdxEAt91D7k

21st Century Skills (4 C’s)

•Critical Thinking•Collaboration•Communication•Creativity

Focus

Shift 1: Focus

Coherence

Shift 2: Coherence

Rigor

Shift 3: Fluency

Shift 4: Deep Understanding

Shift 5: Application

Shift 6: Dual Intensity

Instructional Shifts Combined

Standards for Mathematical Practice

8

Critical Areas- Fifth Grade

Novel Ideas Activity

•List four instructional models/strategies that come to mind for teaching mathematics

Novel Ideas

•Draw a line under your list•At your table group, have each person

share their list• If a shared idea is not on your list, add it

to your list under the line you drew

Overarching Principals of Instructional Design

• Instruction is organized around the solution of meaningful problems

• Instruction provides scaffolds for achieving meaningful learning

Cooper 2006

Overarching Principals of Instructional Design (continued)

• Instruction provides opportunities for ongoing assessment, practice with feedback, revision, and reflection

• The social arrangements of instruction promote collaboration, distributed expertise, and independent learning. Cooper 2006

Instructional Models Continuum

•Mercer and Mercer (2005) suggest that instructional models can be placed along a continuum of choices that range from explicit to implicit instruction.

California Mathematics Framework - p. 9 (2013)

Explicit Instruction Interactive Instruction Implicit Instruction

Explicit Instructional Models

• Support– Practice to mastery– Teaching of discrete skills– Development of skill and procedural

knowledge

Implement Instructional Models

• Link information to students’ background knowledge

• Develop conceptual understanding• Develop problem solving abilities

Explicit Interactive Implicit

Teacher serves as the provider of knowledge

Instruction includes both explicit and implicit methods

Teacher facilitates students learning by creating situations where students discover new knowledge and construct own meaning

Much direct teacher assistance

Balance between direct and non-direct teacher assistance

Non-direct teacher assistance

Teacher regulation of learning

Shared regulation of learning Student regulation of learning

Directed discovery Guided discovery Self-discovery

Direct instruction Strategic instruction Self-regulated instruction

Task Analysis Balance between part-to-whole and whole-to-part

Unit approach

Behavioral Cognitive/metacognitive Holistic

Continuum of Choices

Journal Prompt

After reading the chart, reflect about where the majority of your instruction falls on the continuum.

Think – Pair - Share

•Based on your understanding of the Common Core, where on this continuum do you feel math instruction should be?

CA Mathematics Framework

• Instructional Strategies– http://

www.cde.ca.gov/ci/ma/cf/draft2mathfwchapters.asp

What Does the Framework Say?

•Read Instructional Strategies, Page 1, lines 4-9

Common Core Instruction…

“The purpose of this chapter [training] is not to prescribe the usage of any particular instructional strategy, but to enhance teachers’ repertoire.”

California Mathematics Framework, Instructional Strategies Chapter, p.1

General Instructional Models

• 5 E Model (interactive)-page 10• 3 Phase Model (explicit) – page 10• Singapore Model (interactive)- page 11• Concept Attainment Model (interactive)- page

11• Cooperative Learning Model (implicit)- page

12• Cognitively Guided Instruction (implicit)-

pages 12-13• Problem-Based Learning (interactive)- pages

13-14

Group Presentation

•Choose an instructional model to explore• What is it?• What does it look like?• When is it useful?• What does the teacher do? • What does the student do?• Include citations for any information you

discovered.

Instructional Strategies Specific to the Mathematics Classroom

•Discourse in the Mathematics Classroom• Number Talks• Five Practices for Orchestrating Productive

Mathematics Discussions • Anticipating• Monitoring• Selecting• Sequencing• Connecting

Instructional Strategies Specific to the Mathematics Classroom

•Student Engagement Strategies• Appointment Clock• Carousel-Museum Walk• Charades• Clues• Coming to Consensus• Explorers and Settlers• Find My Rule• Find Your Partner• Four Corners

Instructional Strategies Specific to the Mathematics Classroom

• Student engagement strategies– Give One – Get One– Inside Outside Circle– Jigsaw– KWL

Instructional Strategies Specific to the Mathematics Classroom

• Student engagement strategies– Line up– Making a List– Numbered Heads Together– Partner Up– Quiz, Quiz Trade– Socratic Seminar– Talking Sticks

Instructional Strategies Specific to the Mathematics Classroom (continued)

• Student engagement strategies– Team Share Out– Think Pair Share– Think Write Pair Share– Whip Around– Wrap Around– Y-Chart

Instructional Strategies Specific to the Mathematics Classroom

• Review the instructional strategies• Select one that is new to you and

that you are willing to implement in your classroom or share with a colleague.

• Share with small group– State specific strategy and why you

selected it.

Instructional Strategies Specific to the Mathematics Classroom

• Use of Tools for Mathematics Instruction▫Visual Representations▫Interactive Technology▫Concrete Models▫Concept Maps

•Use of Tasks Incorporating Math Practices

•Use of Real World Problems

Reflection

•How would you structure a lesson around the opening task?

•Refer to your Novel Ideas List, models, and instructional strategies.

•Think about• Standards for Mathematical Practice• 21st Century Skills

•Share with other grade span team

Reflection

• How are you incorporating the Standards for Mathematical Practice into your lesson

• How are you incorporating 21st Century Skills in your lesson?

Putting It All Together

What is the interaction between:•The Continuum•The Models•The Strategies

Outcomes/Agenda• Explore multiple instructional

models that will be required for successful CCSS implementation.

• Discuss a variety of strategies needed to support students in understanding the mathematics being addressed.

• Understand how different instructional strategies support the eight mathematical practices and 21st Century skills.